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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcrcrcrcrcrcrcrcl}\n",
" \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\frac{5}{2} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{29}{10} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{33}{10} x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{14}{5} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{12}{5} x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{16}{5} x_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{13}{5} x_{7} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{8} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{12}{5} x_{9} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{13}{5} x_{10} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{31}{10} x_{11} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} \\frac{5}{2} x_{12} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 250 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 200 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{7} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{8} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 300 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{10} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{11} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{12} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 350 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{10} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 310 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{11} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 330 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{9} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{12} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 320 \\\\\n",
"\\end{array} \\\\\n",
"x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}, x_{9}, x_{10}, x_{11}, x_{12} \\geq 0\n",
"\\end{array}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(120,\\,130,\\,0,\\,0,\\,200,\\,0,\\,0,\\,0,\\,300,\\,190,\\,0,\\,20\\right)$$"
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"(120, 130, 0, 0, 200, 0, 0, 0, 300, 190, 0, 20)"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\texttt{El dual es:}}$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n",
"\\begin{array}{lcrcrcrcrcrcrcrcl}\n",
" \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 250 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 200 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 300 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 350 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 310 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 330 y_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 320 y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{5}{2} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{29}{10} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{33}{10} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{14}{5} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{12}{5} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{16}{5} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{13}{5} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 3 \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{12}{5} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{13}{5} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{31}{10} \\\\\n",
" \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} \\frac{5}{2} \\\\\n",
"\\end{array} \\\\\n",
"y_{1} \\leq 0,\\ y_{2} \\leq 0,\\ y_{3} \\leq 0,\\ y_{4} \\leq 0,\\ y_{5} \\geq 0,\\ y_{6} \\geq 0,\\ y_{7} \\geq 0\n",
"\\end{array}$$"
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"LP problem (use 'view(...)' or '%display typeset' for details)"
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(-\\frac{1}{10},\\,-\\frac{3}{5},\\,-\\frac{1}{10},\\,0,\\,\\frac{13}{5},\\,3,\\,\\frac{5}{2}\\right)$$"
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"(-1/10, -3/5, -1/10, 0, 13/5, 3, 5/2)"
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$"
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"salto"
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$"
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"text/plain": [
"FI"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {\\color{green}{s}}_{1} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 350 \\\\\n",
"{\\color{red}{t}}_{5} & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 310 \\\\\n",
"{\\color{red}{t}}_{6} & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 330 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 320 \\\\\n",
"\\hline\n",
" {W_{ind}} & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 960\n",
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 350 \\\\\n",
"{\\color{red}{t}}_{5} & 0 & -1 & -1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 60 \\\\\n",
"{\\color{red}{t}}_{6} & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 330 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 320 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 710\n",
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{2} & 0 & 1 & 1 & 0 & 1 & 1 & -1 & 0 & 0 & -1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 140 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 350 \\\\\n",
"{x}_{4} & 0 & -1 & -1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 60 \\\\\n",
"{\\color{red}{t}}_{6} & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 330 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 320 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & -1 & -1 & 0 & -1 & -1 & 0 & -1 & -1 & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 650\n",
"\\end{array}\\right)$$"
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"[ x1| 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0|250]\n",
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 110 \\\\\n",
"{x}_{2} & 0 & 1 & 1 & 0 & 1 & 1 & -1 & 0 & 0 & -1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 140 \\\\\n",
"{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 350 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{\\color{red}{t}}_{6} & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 1 & 0 & 1 & 1 & 0 & -1 & -1 & 0 & 0 & -1 & -1 & 0 & 1 & 1 & 0 & 190 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 320 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 510\n",
"\\end{array}\\right)$$"
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"[ x1| 1 0 0 0 -1 -1 1 0 0 1 0 0 0 -1 0 0 -1 0 0 1 0 0|110]\n",
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 110 \\\\\n",
"{x}_{2} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{3} & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 190 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 350 \\\\\n",
"{x}_{4} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{\\color{red}{t}}_{6} & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 80 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 320 \\\\\n",
"\\hline\n",
" {W_{ind}} & 1 & 0 & 0 & 0 & -1 & -1 & 0 & -1 & -1 & 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 400\n",
"\\end{array}\\right)$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 1 & 0 & 1 & 1 & 0 & -1 & -1 & 0 & 0 & -1 & -1 & 0 & 1 & 1 & 0 & 190 \\\\\n",
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"{\\color{green}{s}}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & -1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & -1 & -1 & 0 & 110 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 350 \\\\\n",
"{x}_{4} & 1 & 0 & 1 & 1 & 0 & 1 & 0 & -1 & 0 & 0 & -1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 120 \\\\\n",
"{x}_{5} & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 80 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 320 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 320\n",
"\\end{array}\\right)$$"
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"{x}_{2} & 1 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & -1 & -1 & 0 & -1 & -1 & 0 & 1 & 1 & 0 & 140 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & -1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & -1 & -1 & 0 & 110 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 350 \\\\\n",
"{x}_{4} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"{x}_{5} & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 190 \\\\\n",
"{\\color{red}{t}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 1 & 1 & 1 & 210 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 210\n",
"\\end{array}\\right)$$"
],
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"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7 t5 t6 t7|rhs]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ x7| 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0|300]\n",
"[ x2| 1 1 0 0 0 -1 0 0 -1 1 1 0 0 -1 -1 0 -1 -1 0 1 1 0|140]\n",
"[ x3| 0 0 1 0 0 1 0 0 1 -1 -1 0 1 1 1 0 1 1 0 -1 -1 0|110]\n",
"[ s4| 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0|350]\n",
"[ x4| 1 0 0 1 0 0 0 -1 -1 1 0 0 0 0 -1 0 -1 0 0 1 0 0| 10]\n",
"[ x5| -1 0 0 0 1 1 0 1 1 -1 0 0 0 1 1 0 1 0 0 -1 0 0|190]\n",
"[ t7| 0 0 0 0 0 0 0 0 0 1 1 1 -1 -1 -1 0 -1 -1 -1 1 1 1|210]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ W| 0 0 0 0 0 0 0 0 0 -1 -1 -1 1 1 1 0 1 1 1 0 0 0|210]"
]
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"text": [
"cambio( 5 , 10 )\n"
]
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 130 \\\\\n",
"{x}_{3} & 1 & 0 & 1 & 1 & 0 & 1 & 0 & -1 & 0 & 0 & -1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 120 \\\\\n",
"{\\color{green}{s}}_{4} & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & -1 & 0 & 0 & 340 \\\\\n",
"{x}_{10} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 10 \\\\\n",
"{x}_{5} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{\\color{red}{t}}_{7} & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & -1 & -1 & 0 & 0 & 0 & -1 & -1 & 0 & 1 & 1 & 200 \\\\\n",
"\\hline\n",
" {W_{ind}} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 0 & -1 & -1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 200\n",
"\\end{array}\\right)$$"
],
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"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7 t5 t6 t7|rhs]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ x7| 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0|300]\n",
"[ x2| 0 1 0 -1 0 -1 0 1 0 0 1 0 0 -1 0 0 0 -1 0 0 1 0|130]\n",
"[ x3| 1 0 1 1 0 1 0 -1 0 0 -1 0 1 1 0 0 0 1 0 0 -1 0|120]\n",
"[ s4| -1 0 0 -1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 -1 0 0|340]\n",
"[x10| 1 0 0 1 0 0 0 -1 -1 1 0 0 0 0 -1 0 -1 0 0 1 0 0| 10]\n",
"[ x5| 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|200]\n",
"[ t7| -1 0 0 -1 0 0 0 1 1 0 1 1 -1 -1 0 0 0 -1 -1 0 1 1|200]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ W| 1 0 0 1 0 0 0 -1 -1 0 -1 -1 1 1 0 0 0 1 1 1 0 0|200]"
]
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"text": [
"cambio( 2 , 8 )\n"
]
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 0 & -1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & -1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 170 \\\\\n",
"{x}_{8} & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 130 \\\\\n",
"{x}_{3} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{4} & -1 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & -1 & -1 & 0 & 210 \\\\\n",
"{x}_{10} & 1 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & -1 & -1 & 0 & -1 & -1 & 0 & 1 & 1 & 0 & 140 \\\\\n",
"{x}_{5} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{\\color{red}{t}}_{7} & -1 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 70 \\\\\n",
"\\hline\n",
" {W_{ind}} & 1 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 70\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7 t5 t6 t7|rhs]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ x7| 0 -1 0 1 0 1 1 0 1 0 -1 0 0 1 1 0 0 1 0 0 -1 0|170]\n",
"[ x8| 0 1 0 -1 0 -1 0 1 0 0 1 0 0 -1 0 0 0 -1 0 0 1 0|130]\n",
"[ x3| 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0|250]\n",
"[ s4| -1 -1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 -1 -1 0|210]\n",
"[x10| 1 1 0 0 0 -1 0 0 -1 1 1 0 0 -1 -1 0 -1 -1 0 1 1 0|140]\n",
"[ x5| 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|200]\n",
"[ t7| -1 -1 0 0 0 1 0 0 1 0 0 1 -1 0 0 0 0 0 -1 0 0 1| 70]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ W| 1 1 0 0 0 -1 0 0 -1 0 0 -1 1 0 0 0 0 0 1 1 1 0| 70]"
]
},
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"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 7 , 6 )\n"
]
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"data": {
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & -1 & -1 & 100 \\\\\n",
"{x}_{8} & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & -1 & -1 & 0 & 0 & 0 & -1 & -1 & 0 & 1 & 1 & 200 \\\\\n",
"{x}_{3} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & 140 \\\\\n",
"{x}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 1 & 1 & 1 & 210 \\\\\n",
"{x}_{5} & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 130 \\\\\n",
"{x}_{6} & -1 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 70 \\\\\n",
"\\hline\n",
" {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7 t5 t6 t7|rhs]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ x7| 1 0 0 1 0 0 1 0 0 0 -1 -1 1 1 1 0 0 1 1 0 -1 -1|100]\n",
"[ x8| -1 0 0 -1 0 0 0 1 1 0 1 1 -1 -1 0 0 0 -1 -1 0 1 1|200]\n",
"[ x3| 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0|250]\n",
"[ s4| 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 -1 -1 -1|140]\n",
"[x10| 0 0 0 0 0 0 0 0 0 1 1 1 -1 -1 -1 0 -1 -1 -1 1 1 1|210]\n",
"[ x5| 1 1 0 1 1 0 0 0 -1 0 0 -1 1 1 0 0 0 0 1 0 0 -1|130]\n",
"[ x6| -1 -1 0 0 0 1 0 0 1 0 0 1 -1 0 0 0 0 0 -1 0 0 1| 70]\n",
"[---+---------------------------------------------------------------------------------------+---]\n",
"[ W| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1| 0]"
]
},
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"name": "stdout",
"output_type": "stream",
"text": [
"El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n",
"Preparemos el cuadro inicial de la fase II\n"
]
},
{
"data": {
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""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
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"ry"
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},
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"data": {
"text/html": [
""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$"
],
"text/plain": [
"FII"
]
},
"metadata": {},
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"data": {
"text/html": [
""
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$"
],
"text/plain": [
"ry"
]
},
"metadata": {},
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"data": {
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 100 \\\\\n",
"{x}_{8} & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & -1 & -1 & 0 & 0 & 0 & -1 & -1 & 200 \\\\\n",
"{x}_{3} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 140 \\\\\n",
"{x}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 210 \\\\\n",
"{x}_{5} & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 130 \\\\\n",
"{x}_{6} & -1 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 70 \\\\\n",
"\\hline\n",
" {Z_{ind}} & \\frac{2}{5} & \\frac{2}{5} & 0 & \\frac{4}{5} & 0 & 0 & 0 & 0 & -\\frac{7}{5} & 0 & \\frac{1}{10} & -\\frac{13}{10} & \\frac{1}{2} & \\frac{3}{5} & 0 & 0 & \\frac{13}{5} & 3 & \\frac{19}{5} & 2767\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[------+------------------------------------------------------------------------------------------------------------------------------------+------]\n",
"[ x7| 1 0 0 1 0 0 1 0 0 0 -1 -1 1 1 1 0 0 1 1| 100]\n",
"[ x8| -1 0 0 -1 0 0 0 1 1 0 1 1 -1 -1 0 0 0 -1 -1| 200]\n",
"[ x3| 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0| 250]\n",
"[ s4| 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1| 140]\n",
"[ x10| 0 0 0 0 0 0 0 0 0 1 1 1 -1 -1 -1 0 -1 -1 -1| 210]\n",
"[ x5| 1 1 0 1 1 0 0 0 -1 0 0 -1 1 1 0 0 0 0 1| 130]\n",
"[ x6| -1 -1 0 0 0 1 0 0 1 0 0 1 -1 0 0 0 0 0 -1| 70]\n",
"[------+------------------------------------------------------------------------------------------------------------------------------------+------]\n",
"[ Z| 2/5 2/5 0 4/5 0 0 0 0 -7/5 0 1/10 -13/10 1/2 3/5 0 0 13/5 3 19/5| 2767]"
]
},
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"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 7 , 9 )\n"
]
},
{
"data": {
"text/html": [
""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{7} & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 100 \\\\\n",
"{x}_{8} & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 130 \\\\\n",
"{x}_{3} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 250 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 140 \\\\\n",
"{x}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 210 \\\\\n",
"{x}_{5} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{x}_{9} & -1 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 70 \\\\\n",
"\\hline\n",
" {Z_{ind}} & -1 & -1 & 0 & \\frac{4}{5} & 0 & \\frac{7}{5} & 0 & 0 & 0 & 0 & \\frac{1}{10} & \\frac{1}{10} & -\\frac{9}{10} & \\frac{3}{5} & 0 & 0 & \\frac{13}{5} & 3 & \\frac{12}{5} & 2669\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ x7| 1 0 0 1 0 0 1 0 0 0 -1 -1 1 1 1 0 0 1 1| 100]\n",
"[ x8| 0 1 0 -1 0 -1 0 1 0 0 1 0 0 -1 0 0 0 -1 0| 130]\n",
"[ x3| 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0| 250]\n",
"[ s4| 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1| 140]\n",
"[ x10| 0 0 0 0 0 0 0 0 0 1 1 1 -1 -1 -1 0 -1 -1 -1| 210]\n",
"[ x5| 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0| 200]\n",
"[ x9| -1 -1 0 0 0 1 0 0 1 0 0 1 -1 0 0 0 0 0 -1| 70]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ Z| -1 -1 0 4/5 0 7/5 0 0 0 0 1/10 1/10 -9/10 3/5 0 0 13/5 3 12/5| 2669]"
]
},
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},
{
"name": "stdout",
"output_type": "stream",
"text": [
"cambio( 1 , 1 )\n"
]
},
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 100 \\\\\n",
"{x}_{8} & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 130 \\\\\n",
"{x}_{3} & 0 & 1 & 1 & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & -1 & -1 & 0 & 0 & -1 & -1 & 150 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 140 \\\\\n",
"{x}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 210 \\\\\n",
"{x}_{5} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{x}_{9} & 0 & -1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & -1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 170 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & -1 & 0 & \\frac{9}{5} & 0 & \\frac{7}{5} & 1 & 0 & 0 & 0 & -\\frac{9}{10} & -\\frac{9}{10} & \\frac{1}{10} & \\frac{8}{5} & 1 & 0 & \\frac{13}{5} & 4 & \\frac{17}{5} & 2569\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ x1| 1 0 0 1 0 0 1 0 0 0 -1 -1 1 1 1 0 0 1 1| 100]\n",
"[ x8| 0 1 0 -1 0 -1 0 1 0 0 1 0 0 -1 0 0 0 -1 0| 130]\n",
"[ x3| 0 1 1 -1 0 0 -1 0 0 0 1 1 0 -1 -1 0 0 -1 -1| 150]\n",
"[ s4| 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1| 140]\n",
"[ x10| 0 0 0 0 0 0 0 0 0 1 1 1 -1 -1 -1 0 -1 -1 -1| 210]\n",
"[ x5| 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0| 200]\n",
"[ x9| 0 -1 0 1 0 1 1 0 1 0 -1 0 0 1 1 0 0 1 0| 170]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ Z| 0 -1 0 9/5 0 7/5 1 0 0 0 -9/10 -9/10 1/10 8/5 1 0 13/5 4 17/5| 2569]"
]
},
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},
{
"name": "stdout",
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"text": [
"cambio( 2 , 2 )\n"
]
},
{
"data": {
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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 100 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 130 \\\\\n",
"{x}_{3} & 0 & 0 & 1 & 0 & 0 & 1 & -1 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 20 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 140 \\\\\n",
"{x}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 210 \\\\\n",
"{x}_{5} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{x}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & 0 & \\frac{4}{5} & 0 & \\frac{2}{5} & 1 & 1 & 0 & 0 & \\frac{1}{10} & -\\frac{9}{10} & \\frac{1}{10} & \\frac{3}{5} & 1 & 0 & \\frac{13}{5} & 3 & \\frac{17}{5} & 2439\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ x1| 1 0 0 1 0 0 1 0 0 0 -1 -1 1 1 1 0 0 1 1| 100]\n",
"[ x2| 0 1 0 -1 0 -1 0 1 0 0 1 0 0 -1 0 0 0 -1 0| 130]\n",
"[ x3| 0 0 1 0 0 1 -1 -1 0 0 0 1 0 0 -1 0 0 0 -1| 20]\n",
"[ s4| 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1| 140]\n",
"[ x10| 0 0 0 0 0 0 0 0 0 1 1 1 -1 -1 -1 0 -1 -1 -1| 210]\n",
"[ x5| 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0| 200]\n",
"[ x9| 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0| 300]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ Z| 0 0 0 4/5 0 2/5 1 1 0 0 1/10 -9/10 1/10 3/5 1 0 13/5 3 17/5| 2439]"
]
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"text": [
"cambio( 3 , 12 )\n"
]
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{
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""
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"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrrrrr|r}\n",
"{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {x}_{7} & {x}_{8} & {x}_{9} & {x}_{10} & {x}_{11} & {x}_{12} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n",
"\\hline\n",
" {x}_{1} & 1 & 0 & 1 & 1 & 0 & 1 & 0 & -1 & 0 & 0 & -1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 120 \\\\\n",
"{x}_{2} & 0 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 130 \\\\\n",
"{x}_{12} & 0 & 0 & 1 & 0 & 0 & 1 & -1 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 20 \\\\\n",
"{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 140 \\\\\n",
"{x}_{10} & 0 & 0 & -1 & 0 & 0 & -1 & 1 & 1 & 0 & 1 & 1 & 0 & -1 & -1 & 0 & 0 & -1 & -1 & 0 & 190 \\\\\n",
"{x}_{5} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 200 \\\\\n",
"{x}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 300 \\\\\n",
"\\hline\n",
" {Z_{ind}} & 0 & 0 & \\frac{9}{10} & \\frac{4}{5} & 0 & \\frac{13}{10} & \\frac{1}{10} & \\frac{1}{10} & 0 & 0 & \\frac{1}{10} & 0 & \\frac{1}{10} & \\frac{3}{5} & \\frac{1}{10} & 0 & \\frac{13}{5} & 3 & \\frac{5}{2} & 2421\n",
"\\end{array}\\right)$$"
],
"text/plain": [
"[ B| x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 s1 s2 s3 s4 s5 s6 s7| rhs]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ x1| 1 0 1 1 0 1 0 -1 0 0 -1 0 1 1 0 0 0 1 0| 120]\n",
"[ x2| 0 1 0 -1 0 -1 0 1 0 0 1 0 0 -1 0 0 0 -1 0| 130]\n",
"[ x12| 0 0 1 0 0 1 -1 -1 0 0 0 1 0 0 -1 0 0 0 -1| 20]\n",
"[ s4| 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1| 140]\n",
"[ x10| 0 0 -1 0 0 -1 1 1 0 1 1 0 -1 -1 0 0 -1 -1 0| 190]\n",
"[ x5| 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0| 200]\n",
"[ x9| 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0| 300]\n",
"[-----+-----------------------------------------------------------------------------------------------------------------+-----]\n",
"[ Z| 0 0 9/10 4/5 0 13/10 1/10 1/10 0 0 1/10 0 1/10 3/5 1/10 0 13/5 3 5/2| 2421]"
]
},
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},
{
"name": "stdout",
"output_type": "stream",
"text": [
"El problema es óptimo\n"
]
}
],
"source": [
"tipo='min' # max o min\n",
"\n",
"n=12 # número de variables x's\n",
"m=7 # número de restricciones (distintas de las de signo)\n",
"\n",
"c=matrix(QQ,1,n,[2.5,2.9,3.3,2.8,2.4,3.2,2.6,3,2.4,2.6,3.1,2.5] ) # vector de costos\n",
"\n",
"A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n",
"[1,1,1,0,0,0,0,0,0,0,0,0],\n",
"[0,0,0,1,1,1,0,0,0,0,0,0],\n",
"[0,0,0,0,0,0,1,1,1,0,0,0],\n",
"[0,0,0,0,0,0,0,0,0,1,1,1],\n",
"[1,0,0,1,0,0,1,0,0,1,0,0],\n",
"[0,1,0,0,1,0,0,1,0,0,1,0],\n",
"[0,0,1,0,0,1,0,0,1,0,0,1]\n",
"])\n",
"\n",
"b=matrix(QQ,m,1,[250,200,300,350,310,330,320]) # vector de la derecha\n",
"\n",
"\n",
"h=matrix(ZZ,1,m,[1,1,1,1,-1,-1,-1]) # variables de holgura: \n",
" # Pon 1 si va sumando, \n",
" # -1 si va restando y \n",
" # 0 si no hay variable de holgura.\n",
"#######################################################\n",
"\n",
"load('https://sage.unex.es/501708/simplex2023Auto.sage')\n",
"#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n",
"#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n",
"\n"
]
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